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For the storage process $Q_{B_H}(t)=\\sup_{-\\infty\\le s\\le t} \\left(B_H(t)-B_H(s)-c(t-s)\\right)$ we show that, for any $T(u)>0$ such that $T(u)=o(u^\\frac{2H-1}{H})$, \\[\\mathbb P (\\inf_{s\\in[0,T(u)]} Q_{B_H}(s)>u)\\sim\\mathbb P(Q_{B_H}(0)>u),\\quad\\text{as}\\quad u\\to\\infty.\\] This finding, known in the literature as the strong Piterbarg property, is in line with previously observed properties of storage processes with self-similar and infinitely divisible input without Gaussian component."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.1496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-05T17:20:45Z","cross_cats_sorted":[],"title_canon_sha256":"69ebe5c20783b28d4ceffc3d5a8bc6c257efe8934057180b3cd8a83e001e797d","abstract_canon_sha256":"3585cf0db04f8a58df718ef94e3873b0eb75f6828fb243fa497bccb57a063c67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.267398Z","signature_b64":"oM8bCIMSXkJAgdRipcMTRCunSeyJCc78NcOwcoXVJQGPt9zp6OvFCgc0QHSY0BGNOdagnpEXba77J1rpaQ3CDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d4ce69c4019506586b39de6406f0047f31e98c6d4db57dbe2ce6a2b49e017a3","last_reissued_at":"2026-05-18T02:43:24.266995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.266995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the infimum attained by the reflected fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosi\\'nski, Krzysztof D\\k{e}bicki","submitted_at":"2013-10-05T17:20:45Z","abstract_excerpt":"Let $\\{B_H(t):t\\ge 0\\}$ be a fractional Brownian motion with Hurst parameter $H\\in(\\frac{1}{2},1)$. For the storage process $Q_{B_H}(t)=\\sup_{-\\infty\\le s\\le t} \\left(B_H(t)-B_H(s)-c(t-s)\\right)$ we show that, for any $T(u)>0$ such that $T(u)=o(u^\\frac{2H-1}{H})$, \\[\\mathbb P (\\inf_{s\\in[0,T(u)]} Q_{B_H}(s)>u)\\sim\\mathbb P(Q_{B_H}(0)>u),\\quad\\text{as}\\quad u\\to\\infty.\\] This finding, known in the literature as the strong Piterbarg property, is in line with previously observed properties of storage processes with self-similar and infinitely divisible input without Gaussian component."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1496","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.1496","created_at":"2026-05-18T02:43:24.267052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.1496v2","created_at":"2026-05-18T02:43:24.267052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1496","created_at":"2026-05-18T02:43:24.267052+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVGONHCADFIG","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVGONHCADFIGLBVT","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVGONHCA","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7","json":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7.json","graph_json":"https://pith.science/api/pith-number/DVGONHCADFIGLBVTTXTEA3YAI7/graph.json","events_json":"https://pith.science/api/pith-number/DVGONHCADFIGLBVTTXTEA3YAI7/events.json","paper":"https://pith.science/paper/DVGONHCA"},"agent_actions":{"view_html":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7","download_json":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7.json","view_paper":"https://pith.science/paper/DVGONHCA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.1496&json=true","fetch_graph":"https://pith.science/api/pith-number/DVGONHCADFIGLBVTTXTEA3YAI7/graph.json","fetch_events":"https://pith.science/api/pith-number/DVGONHCADFIGLBVTTXTEA3YAI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7/action/storage_attestation","attest_author":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7/action/author_attestation","sign_citation":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7/action/citation_signature","submit_replication":"https://pith.science/pith/DVGONHCADFIGLBVTTXTEA3YAI7/action/replication_record"}},"created_at":"2026-05-18T02:43:24.267052+00:00","updated_at":"2026-05-18T02:43:24.267052+00:00"}